Since the OP brought 12 gauge energy into the post I think it's only fair to point out some oranges in the apple basket.
A popular load for SD is the 9 pellet 12 gauge Tactical aka low recoil load. A common load is 9 pellets of 53 gr. OObuck @ 1145 fps. (Fed PD132) for 1388 ft. lbs.
Compared to Fed. 3" 20 gauge 18 pellets of 29 gr. #2Buck @ 1100 fps. for 1402 ft. lbs. The 20 gauge load comes out on top in terms of power by a whopping 14 ft. lbs.
Now we can look at 9 .33" wide holes vs. 18 .27" holes. Since the OP is basing his argument on muzzle energy and discounting penetration caused by differences in sectional density it appears that the 20 gauge now comes out on top.
Assuming the pellets do not deform (just to simplify things), the OObuck pellet has a 2D surface area of .5185" and the #2Buck has .4242" Total possible surface area for leakage is 4.6665" for OOBuck and 7.6367" for #2Buck. The 20gauge still comes out on top. Real life shows that the 12 gauge pellets do in fact go deeper but now it comes down to which is more likely to hit important things and cause more leaks.
To further obfuscate matters, #3Buck in a 20 gauge is stacked in layers of 4; just like #1 buck in common 12 gauge loads. #2Buck is stacked in layers of 3 just like OOBuck in a 12 gauge. Which one patterns better in YOUR gun? Pellets that miss don't put energy on target. Lots of ink has been spilled on these pages abut how #1Buck 12 gauge loads don't pattern well; a casual reader might extrapolate that to mean #3Buck won't pattern in a 20 gauge either.
Also, plenty of ink has been spilled on how the lower velocity loads pattern better than the high velocity loads. Again extrapolating an assumption about performance would lead some to conclude that the slower 3" 20 gauge load may pattern better.
All of this boils down to what does YOUR gun pattern better, what do YOU shoot better, and what does real world terminal performance tell us? All too much has been made of muzzle energy. What counts is how many holes go how deep and hit how many important things along the way.